Balanced 2^m factorial designs of resolution v which allow search and estimation of one extra unknown effect, 4 ≤ m ≤ 8

Abstract

In this paper, we obtain balanced resolution V plans for 2^m factorial experiments (4 ≤ m ≤ 8), which have an additional feature. Instead of assuming that the three factor and higher order effects are all zero, we assume that there is at most one nonnegligible effect among them; however, we do not know which particular effect is nonnegligible. The problem is to search which effect is non-negligible and to estimate it, along with estimating the main effects and two factor interactions etc., as in an ordinary resolution V design. For every value of N (the number of treatments) within a certain practical range, we present a design using which the search and estimation can be carried out. (Of course, as in all statistical problems, the probability of correct search will depend upon the size of “error” or “noise” present in the observations. However, the designs obtained are such that, at least in the noiseless case, this probability equals 1.) It is found that many of these designs are identical with optimal balanced resolution V designs obtained earlier in the work of Srivastava and Chopra.

Keywords:

• linear models
• balanced arrays
• search designs
• optimal designs